🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{1}{7} + \frac{4}{7} \div \frac{10}{11}$$ and write the answer in its simplest form. 2. **Recall the division rule for frac

1. **State the problem:** We want to find how many years it will take for the population of an island to double if it increases by 10% each year. 2. **Formula used:** The populatio

1. The problem is to simplify the expression with the addition of 4. 2. Since the original expression is not provided, we assume the problem is to add 4 to a given number or expres

1. **State the problem:** Solve the quadratic equation $$-2x^2 + 4x - 4 = 0$$ by completing the square. 2. **Rewrite the equation:** First, divide the entire equation by -2 to make

1. **Problem:** Simplify the expression $ (3x + 5) + (2x + 7) $. 2. **Formula and rules:** When adding polynomials, combine like terms by adding their coefficients.

1. **Problem statement:** We need to find the smallest number of fence pieces to surround a rectangular garden measuring 3 m by 6 m without cutting or bending any fence pieces. 2.

1. **State the problem:** We need to find the exponential function $f(x)$ that fits the given graph. 2. **Identify key points:** From the graph, the function passes through $(0,5)$

1. **State the problem:** We are given an exponential graph with a point (0,5) and asked to find the exponential function $f(x)$, including the initial value and constant ratio. 2.

1. **State the problem:** Find the value of each expression when $p=2$. 2. **Evaluate (a) $6p - 10$:**

1. **State the problem:** We want to find what percent the new value 200 is of the original price 10.

1. **Problem statement:** Given tables of values for two exponential functions, find the constant ratio, initial value, and write the exponential function $f(x)$ for each. ---

1. Muammo: Agar $2017a - 2018b = 1$ bo'lsa, $\gcd(a,b)$ ni toping. 2. Bu tenglama $2017a - 2018b = 1$ ko'rsatadiki, $a$ va $b$ sonlari $2017$ va $2018$ sonlari bilan lineer kombina

1. **State the problem:** Solve the equation $3 = 0$. 2. **Analyze the equation:** The equation $3 = 0$ is a simple equality statement.

1. The problem states that the $n^{th}$ term of a sequence is given by the formula $a_n = 4n^2$. 2. We need to find the first three terms of the sequence, which means we will calcu

1. **State the problem:** Simplify the expression $$\frac{2x^2 - 8}{4x}$$. 2. **Write the formula and rules:** To simplify a rational expression, factor numerator and denominator a

1. Problem: Convert the simultaneous linear equations into matrix form. 2. The matrix form of simultaneous linear equations $ax + by = c$ and $dx + ey = f$ is:

1. **State the problem:** Determine which category correctly describes the number $\sqrt{5}$. The options are: A. whole number

1. **State the problem:** อลิสมีเงินได้สุทธิ 560,000 บาท และถูกหักภาษี ณ ที่จ่าย 7,000 บาท ต้องหาว่าเมื่อยื่นแบบแสดงรายการภาษีเงินได้ จะต้องชำระภาษีเพิ่มหรือได้รับเงินภาษีคืนเท่าไร

1. Muammo: Sizdan algebraik ifodani yechish yoki hisoblash so'ralmoqda. 2. Formulalar va qoidalar: Muammo aniq ko'rsatilmagan, shuning uchun iltimos, aniq masalani taqdim eting.

1. **State the problem:** Solve the inequality $$\frac{2x - 5}{x + 3} \geq 1$$. 2. **Rewrite the inequality:** Subtract 1 from both sides to get a single rational expression:

1. The problem involves understanding the function $f(a)$ defined as: $$